Integrate the function frac{1}{x-sqrt{x}}. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given integral is $I = \int \frac{1}{x-\sqrt{x}} dx$. We can rewrite the denominator as $\sqrt{x}(\sqrt{x}-1)$. So,$I = \int \frac{1}{\sqrt{x}

Vedclass · Accepted Answer

$2 \log |\sqrt{x}-1| + C$

Vedclass · Answer

(A) The given integral is $I = \int \frac{1}{x-\sqrt{x}} dx$. We can rewrite the denominator as $\sqrt{x}(\sqrt{x}-1)$. So,$I = \int \frac{1}{\sqrt{x}(\sqrt{x}-1)} dx$. Let $t = \sqrt{x}-1$. Then,$dt = \frac{1}{2\sqrt{x}} dx$,which implies $\frac{dx}{\sqrt{x}} = 2 dt$. Substituting these into the integral,we get $I = \int \frac{2}{t} dt$. Integrating with respect to $t$,we obtain $I = 2 \log |t| + C$. Substituting back $t = \sqrt{x}-1$,we get $I = 2 \log |\sqrt{x}-1| + C$,where $C$ is an arbitrary constant.

Integrate the function $\frac{1}{x-\sqrt{x}}$.

Similar Questions

$\int {\frac{{1 - {x^7}}}{{x(1 + {x^7})}}} \,dx$ equals

$\int \frac{x^2}{1+x^6} d x$ is equal to

Integrate the function: $\frac{x^{3}}{\sqrt{1-x^{8}}}$

Integrate the function $\frac{x}{9-4x^{2}}$.

$\int \sqrt{e^x-1} \, dx =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module